Theoretical characterisation of magnetic force microscope tip stray fields
A large part of the work described in this thesis is concerned with a theoretical characterisation of Magnetic Force Microscope (MFM) tip stray fields. The remainder of the thesis is concerned with a theoretical investigation of the accuracy of a practical method for characterising the MFM tip field - i.e. the electron tomography reconstruction method.
The thesis begins with a brief discussion of the fundamentals of ferromagnetism and the importance of being able to determine the magnetic structure of a material.
The second chapter considers several different methods which have been developed for determining the magnetic configuration of a material and particular attention is given to Differential Phase Contrast (DPC) Lorentz microscopy (this technique is the basis for three dimensional reconstruction of a MFM tip stray field using electron beam tomography) and Magnetic Force Microscopy. In the case of the latter a discussion of the need to characterise the MFM tip field is given.
The fundamental principles and the application of electron beam tomography for the investigation of MFM tip fields are discussed in Chapter 3. Two reconstruction algorithms - the Algebraic Reconstruction Technique (ART) and the Radon Transform Method (RTM) - are considered. The latter reconstruction technique is considered in more detail since it is used predominately in this thesis. The acquisition of the experimental data sets for tomographic reconstruction is also described in this chapter.
In Chapter 4 a theoretical investigation of the effect on the tip stray field of varying several physical tip characteristics is carried out. A tip model is constructed and its shape, height and the thickness of the film coating are all varied and the resulting tip stray field and line scan deflection data sets are investigated. A comparison of the deflection data generated by the tip model and that generated by a practical MFM tip is also carried out. It is found that the simulated deflection data from the tip model compared favourably with the experimental deflection data; however there is found to be a contribution to the experimental deflection data sets for which the tip model does not account. Nonetheless, comparison of the experimental and simulated deflection data gave encouragement to extend the modelling to the cantilever and substrate portions of the tip assembly.
In Chapter 5 the deflection data sets generated by a practical MFM tip magnetised in two separate cases is considered. Tip, cantilever and substrate models were constructed for each case and the simulated deflection data was found to compare favourably with the deflection data generated by the practical tip assembly. A theoretical investigation into the character of the stray field from the cantilever and substrate portions of the tip assembly is undertaken and the conclusion is that the magnitude of the stray field from the cantilever and substrate is small in the vicinity of the tip but is spread over a large distance and as a result contributes greatly to the deflection data generated by the MFM tip assembly.
In Chapter 6, a theoretical investigation of the effect on the accuracy of the RTM reconstructed stray field that the cantilever and substrate contribution to the MFM tip assembly's deflection data set is undertaken. It is found that although the RTM reconstruction method can produce a relatively accurate representation of the MFM tip field, the cantilever and substrate contribution does reduce the accuracy of the reconstructed tip field. Two separate methods for reducing the error in the reconstructed tip field are considered. It is found that these methods produce very accurate representations of the tip field even when the exact cantilever and substrate contribution is not known. The accuracy of the tip assembly's stray field reconstructed using the ART is also considered and it is found that ART does not produce as accurate a representation of the MFM tip field as is obtained using RTM. The effect of the electron probe size and the manual alignment of the deflection line scans on the accuracy of the reconstructed stray field are also investigated.
In Chapter 7 two more MFM tips of a distinct physical character are modelled and their stray fields and deflection data sets are investigated.
Conclusions and suggestions for further work are given in Chapter 8.